we have had good luck storing potatoes and carrots by packing them in slightly moist sand. I use large plastic tubs, clean sand and pack them in layers. Put a loose cardboard cover over the tub to keep the light out.
We have also mulched carrots over the winter, leave them in the ground covered with a foot of hay; pull back the hay and dig when you need carrots. This might works with potatoes, has anyone done this?